26 I KINEMATICS OF A POINT. LAWS OF MOTION. 



are called positional forces, those of the latter motional forces. As 

 an example of the latter, we know that a body moving through the 

 air experiences a negative acceleration which is greater the greater 

 the velocity of the body, and we say that the motion is retarded hy 

 a force, which we call the resistance of the air. 



Supposing now X, Y, Z to be given functions of the coordinates 

 and velocities, the integration of the differential equations 41) con- 

 stitutes the problem of the mechanics of a single particle. It is in 

 this sense that the problems of mechanics in general are to be 

 considered. (See Note I.) 



Returning to the "change of motion" mentioned in the second 

 law, it is customary to characterize the product of the mass by the 

 vector velocity as the momentum of the body, a vector whose 

 components are 



A^\ -n/r dx -~,r dy -,.- dz 



42) JCrrr*it< M = m dl' M > = m w 



This is the motus whose rate of change measures the force, so that 

 equations 41) may be written 



dM dM 



14. Units. The specification of any quantity, scalar or vector, 

 involves two factors, first a numerical quantity or numeric, and 

 secondly a concrete quantity in terms of which all quantities of that 

 kind are numerically expressed, called a unit. The simplest unit is 

 that of the geometrical quantity, length. We shall adopt as the 

 unit of length the centimeter, defined as the one -hundredth part of 

 the distance at temperature zero degrees Centigrade, and pressure 

 760 millimeters of mercury, between two parallel lines engraved on 

 a certain bar of platinum -iridium alloy, deposited in a vault in the 

 laboratory of the "Comite International des Poids et Mesures", at 

 Sevres, near Paris. This bar is known as the ({ Metre Prototype", 

 and serves as the basis of length measurements for the civilized world J ) 

 (except the British Empire and Russia 2 ). 



It was proposed by Maxwell to use a natural unit of length, 

 namely the length of a wave of light corresponding to some well 

 defined line in the spectrum of some element, at a definite temperature 

 and pressure, as it is highly probable that such a wave-length is 

 extremely constant. Measurements were carried out at Sevres by 

 Michelson, with this end in view, which established the ratio between 



1) See Gnillamne, La Convention chi Metre. 



2) The United States yard is defined as 3600/3937 meters. 



